A Cahn–Hilliard Model Based on Microconcentrations

Samuel Forest (1) , Alain Miranville (2)

1 CDM - Centre des Matériaux
2 DACTIM-MIS - Data Analysis and Computations Through Imaging Modeling-Mathématiques, Imagerie, Santé

Our aim in this paper is to study a Cahn-Hilliard type system based on microconcentrations. We prove the existence and uniqueness of solutions to this system and then prove the convergence of the solutions to those of the original Cahn-Hilliard equation as a small parameter goes to zero, on finite time intervals.

Mots clés: Cahn-Hilliard model; microconcentrations; well-posedness; convergence to the Cahn-Hilliard equation

Domaines: Mathématiques [math]; Physique [physics]; Sciences de l'ingénieur [physics]

Samuel Forest, Alain Miranville. A Cahn–Hilliard Model Based on Microconcentrations. Mediterranean Journal of Mathematics, 2023, 20 (4), pp.223. ⟨10.1007/s00009-023-02430-1⟩. ⟨hal-04106941⟩